Irreducible representations of a class of unbounded operator algebras

Irreducible Representations of Operator Algebras

Bicommutants of Reduced Unbounded Operator Algebras

The unbounded bicommutant (ME′ ) ′′ wc of the reduction of an O*algebra Mvia a given projection E weakly commuting with M is studied, with the aim of finding conditions under which the reduction of a GW*-algebra is a GW*-algebra itself. The obtained results are applied to the problem of the existence of conditional expectations on O*-algebras.

Irreducible Representations of Twisted Multiloop Algebras

We describe the finite-dimensional simple modules of all the twisted multiloop algebras and classify them up to isomorphism.

Constructing Irreducible Representations of Finitely Presented Algebras

We describe an algorithmic test, using the “standard polynomial identity” (and elementary computational commutative algebra), for determining whether or not a finitely presented associative algebra has an irreducible n-dimensional representation. When ndimensional irreducible representations do exist, our proposed procedure can (in principle) produce explicit constructions.

Irreducible Representations of Inner Quasidiagonal C*-algebras

It is shown that a separable C*-algebra is inner quasidiagonal if and only if it has a separating family of quasidiagonal irreducible representations. As a consequence, a separable C*-algebra is a strong NF algebra if and only if it is nuclear and has a separating family of quasidiagonal irreducible representations. We also obtain some permanence properties of the class of inner quasidiagonal C...